Mike Krebs

Teaching

• Class websites

Publications

• My Ph.D. dissertation
• Toledo invariants of Higgs bundles on elliptic surfaces associated to base orbifolds of Seifert fibered homology 3-spheres. (Appears in Michigan Math. J. Volume 56, Issue 1 (2008), 3-27.)
• On the Spectra of Johnson Graphs. Joint work with A. Shaheen. (Appears in Electronic Journal of Linear Algebra, Volume 17, pp. 154-167, March 2008)
• Think Around The Box, a crossword puzzle of sorts. The Mathematical Intelligencer, Volume 31, Number 2, 59-60.
• I'm the faculty adviser for Fixed Points of Number Derivatives Modulo n by CSULA student F. Bains. Rose-Hulman Undergraduate Math Journal, Vol. 10 (2009), Issue 1.
• How to differentiate an integer modulo n. Joint work with C. Emmons and A. Shaheen. College Mathematics Journal, November 2009.
• On Cantor's first uncountability proof, Pick's theorem, and the irrationality of the golden ratio. Joint work with T. Wright. Amer. Math. Monthly 117 (2010), no. 7, 633-637
• mini-Sudokus and Groups. Joint work with C. Arcos (CSULA student) and G. Brookfield. Math. Mag. 83 (2010), no. 2, 111-122
• Expander Families and Cayley Graphs: A Beginner's Guide, co-authored by A. Shaheen, Oxford University Press, New York, Oct. 2011
• K-quasiderivations. (K-quasiderivations are maps that satisfy both the Product Rule and Chain Rule.) Central European Journal of Mathematics, Vol. 10 (2012), no. 2, 824-834
• A combinatorial trace method: Counting closed paths to assay graph eigenvalues. Joint work with K. Dsouza (CSULA student). Rocky Mountain Journal of Mathematics, Vol. 43 (2013), no. 2, 469-478
• Simple examples of the combinatorial trace method in action. Joint work with N. Martinez (CSULA student). College Mathematics Journal, Vol. 44 (2013), no. 1, 32-36
• Expander families, group structure, and semidirect products. Joint work with M. Aivazian (CSULA student). Bulletin of the Irish Mathematical Society, Number 71 (2013), 21-30
• Expander graphs. In J. Gross and J. Yellen (Eds.), Handbook of Graph Theory, Second Edition. CRC Press, 2013.
• ZERO SUMS ON UNIT SQUARE VERTEX SETS, AND PLANE COLORINGS. Joint work with R. Katz and A. Shaheen. The American Mathematical Monthly. Vol. 121, No. 7 (August-September 2014), pp. 610-618.
• Al Fares, A. (CSULA student), E. Golvin (CSULA student), M. Krebs. A class of 2-groups of derived length three. Serdica Mathematical Journal, Volume 41, Numbers 2-3, 2015, pp. 329-332
• Kevin Cramer (CSULA student), Mike Krebs, Nicole Shabazi (CSULA student), Anthony Shaheen and Edward Voskanian (CSULA student). The Isoperimetric constant and Kazhdan constant of a Paley graph, Involve, 9(2): 293-306, March 2016.
• On cardinalities and compact closures.  Applied General Topology, 18(1): 107, April 2017, 107-115
• Can a Subset's Topology Detect Continuous Extensions?  The College Mathematics Journal, 49(2): 138-139, March 2018.
• Finite epsilon unit-distance graphs.  Journal of Algebra, Combinatorics, Discrete Structures, and Applications, Sept. 2021; 8(3): 161-166
• What Baseball Team Does PageRank Say Was The Best Ever?, Baseball Research Journal, Spring 2022.  Joint work with Cal State LA student Gwen Ostergren
• Clique numbers of finite unit-quadrance graphs, Journal of Algebraic Combinatorics, 57, 1-20 (2023)
• Kazhdan constants and isomorphic graph pairs, joint work with Cal State LA students M. Davila, T. Hayes, M. Krebs, and M. Reyes.  Algebra and Discrete Mathematics, Volume 35 (2023). Number 1, pp. 73-85.
• Chromatic numbers of Cayley graphs of abelian groups: A matrix method, joint work with Cal State LA student J. Cervantes.  Linear Algebra Appl. (2023).  In press. (The arXiv version this links to corrects an error in an example that appears in the published version.)
• Authors' Notes for "Chromatic numbers of abelian Cayley graphs: A matrix method"  (bonus content: a Mathematica file with code for computing the chromatic number of a standardized abelian Cayley graph associated to a 1 x r, m x 1, 2 2 x 2, or 3 x 2 matrix.)

Presentations

• How to Put Rainbow Sprinkles on a Donut: Chromatic Numbers of Abelian Cayley Graphs

Other, random stuff

• A group of Cal State LA students on the My Favorite Theorem podcast
• Silly math videos I've made
• Bizarre and/or mediocre songs I've made

I graduated from Johns Hopkins University in May 2005. My thesis advisor was Dr. Richard Wentworth.

This website was last updated in May 2022.